So I haven't played Minecraft since.. 1.2? I think somewhere along those lines.
What have I missed out on? What are the main things they have added since then, and what else should I know about?
You have missed out on a lot.
1.3 - Untitled - Villager trading and emeralds, and command blocks - they run commands when redstone activated.
1.4 - Pretty Scary Update - Bats, witches, wither skeletons, and a completely new boss, the Wither!
1.5 - Redstone Update - Comparators, redstone blocks, daylight sensors, and nether quartz.
1.6 - Horse Update - TNT mine carts, horses, stained clay, and coal blocks, among other miscellaneous things.
1.7 - The Update That Changed the World - Added like 20 million new biomes, new flowers, stained glass, and other stuff.
1.8 - Upcoming (try the development versions!) - Slime blocks, lots of new, really cool commands, and water dungeons.
Version history on the Minecraft wiki.As I said, there's a new launcher. The old one won't work anymore. You can use the launcher to test out development versions (snapshots), currently the 1.8 snapshots, to try out the new features. Adventure maps are now completely different, thanks to command blocks. You can do some INSANE stuff with them, I can only imagine what some of the 1.8 magic would look like to a 1.2 user.
Meanwhile, modded Minecraft has gotten way more popular, way more accessible, and way COOLER. I won't talk about it much, but you can always check out the FTB wiki.